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On the Recovery of Analytic Functions

Published online by Cambridge University Press:  20 November 2018

Joseph A. Cima  and
Michael Stessin
Joseph A. Cima
Affiliation:
Deptartment of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599, U.S.A.
Michael Stessin
Affiliation:
Deptartment of Mathematics and Statistics, SUNY at Albany, Albany, New York 12222, U.S.A.
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Abstract

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In this paper we consider questions of recapturing an analytic function in a Banach space from its values on a uniqueness set. The principal method is to use reproducing kernels to construct a sequence in the Banach space which converges in norm to the given functions. The method works for several classical Banach spaces of analytic functions including some Hardy and Bergman spaces.

Keywords

30D5030D5532A35
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 2 , 01 April 1996 , pp. 288 - 301
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. Anderson, J.T. and Cima, J.A., Recovering HP functions from partial boundary data. J. Complex Anal., to appear.Google Scholar
2. Carleman, T.,Lesfonctions quasi-analytiques, Gauthier-Villars, Paris, 1926.Google Scholar
3. Cima, J.A., MacGregor, T.H. and Stessin, M.I., Recapturing functions in YP spaces. Indiana Univ. Math. J., 43 (1994)205-220.Google Scholar
4. Dunford, N. and Schwartz, J.T.,Linear Operators, Part I, Wiley-Interscience, New York, 1958.Google Scholar
5. Gabriel, R.M., An inequality concerning the integrals of positive subharmonic functions along certain circles. London Math. Soc. J. (18) 5 (1930), 129–131.Google Scholar
6. Horowitz, C.A., Zeros of functions in the Bergman space.Duke Math. J. 41 (1974), 693–710.Google Scholar
7. Ya.|Khavinson, S., Two papers on extremal problems in complex analysis. Trans. Amer. Math. Soc. (2) 129 (1986).Google Scholar
8. Patil, D.J., Representation of HP functions. Bull. Amer. Math. Soc. 78 (1972), 617–620.Google Scholar
9. Riesz, F., Ueber die Randwerte einer Analytischen Funktion. Math. Z. 18 (1922).Google Scholar
10. Walsh, J.L., Interpolation and approximation by rational functions in the complex domain. In: Amer. Math. Soc. Colloquium Publications, 3rd edition 20, 1960.Google Scholar